Kerala University 2005 B.C.A Computer Application survey - Question Paper
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(Pages: 2) K 5184
SIXTH SEMESTER B.C.A. (VOCATIONAL COURSE) DEGREE EXAMINATION FEBRUARY/MARCH 2005
Optional SubjectStatistics Paper XISAMPLE SURVEY Time : Three Hours Maximum : 90 Marks
Not more than 30 marks will be awarded from each of the three units.
Unit I
1. Explain the following terms : Sampling frame, Sampling design and Sampling unit.
(6 marks)
2. Distinguish between Population and Sample. Also describe the need for census survey and sample survey giving illustrative examples.
(6 marks)
3. What are the different stages in a sample survey ? Describe with examples. (4 marks)
4. Distinguish between Random sampling and Non-random sampling. Bring out the advantages and disadvantages of each.
. - - (6 marks)
5. Define a Simple random sample without replacement. Show that the probability of selecting a specified unit in any draw is the same in SRSWOR.
(7 marks)
6. A population consists of 5 units with values 50, 52, 48, 58, 55. Iiit all possible samples of size 2 by SRSWOR, Hence show that the sample mean is an unbiased estimator of the population mean.
(7 marks)
7. In an SRSWOR from a finite population, show that the sample mean is unbiased for population mean. Derive the expression for the variance of the estimate.
(8 marks)
8. Obtain the expression for the optimum sample size for a specified precision while estimating the mean under SRSWOR.
(6 marks)
Unit II
9. Explain the use of auxiliary information in sample surveys using an example.
(5 marks)
0. What is the ratio estimate of the population ratio ? Obtain an expression for its bias.
(6 marks)
11. Derive an expression for the relative bias of the ratio estimator in SRSWOR.
(7 marks)
12. Compare the ratio estimator with mean per unit and derive a condition under which the ratio estimator is superiorto the mean per unit.
(7 marks)
13. Under usual notation, show that Vran (y) Vprop (y) Vt (y gt). (8 marks)
14. Explain the concept of stratified sampling. What are the principles of stratification ? Bring out the advantages.
(S marks)
15. Find the expression for the variance of the estimator under stratified random sampling.
(6 marks)
16. What is the usual regression estimator for the population mean ? Obtain an expression for its sampling variance.
(6 marks)
Unit III
17. Distinguish between Linear and Circular systematic samples. (6 marks)
18. Explain how systematic sample can be regarded as a cluster sample. (5 marks)
19. Distinguish between Multistage and Multiphase sampling, through.illustrative examples.
(6 marks)
20. Obtain an expression for the variance of the unbiased estimator y# under systematic sampling vith N nk.
(7-ffiarE3T
21. Compare the efficiencies of the estimators of the population mean under stratified and cluster sampling.
(6 marks)
22. Distinguish between Samjfling and Non-sampling errors. How they are controlled ?
(6 marks)
23. A sample survey was conducted for estimating the number of palm trees in a Taluk with 72 villages. A sample of 8 villages was selected with SRSWOR and from each village a sample of 4 clusters of 20 fields with SRSWOR The data is as given below.
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Village No. of clusters Number of Palm trees in clusters | |||||||||||||||||||||||||||||||||||||||||||||
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Obtain an unbiased estimator of the total number of palm trees in the Taluk. (7 marks)
24. Explain how a circular systematic sample is selected. Write down all circular systematic samples of size 4 from a population of 15 units.
(7 marks)
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| Earning: Approval pending. |
